Package org.apache.commons.math.optimization.fitting

Class ParametricGaussianFunction

java.lang.Object

org.apache.commons.math.optimization.fitting.ParametricGaussianFunction

All Implemented Interfaces:

Serializable, ParametricRealFunction

public class ParametricGaussianFunction
extends Object
implements ParametricRealFunction, Serializable

A Gaussian function. Specifically:

f(x) = a + b*exp(-((x - c)^2 / (2*d^2)))

The parameters have the following meaning:

• a is a constant offset that shifts f(x) up or down
• b is the height of the peak
• c is the position of the center of the peak
• d is related to the FWHM by FWHM = 2*sqrt(2*ln(2))*d

Notation key:

• x^n: x raised to the power of n
• exp(x): e^x
• sqrt(x): the square root of x
• ln(x): the natural logarithm of x

References:

• Wikipedia: Gaussian function

Since:

2.2

See Also:

Serialized Form

Constructor Summary

Constructors

Constructor	Description
ParametricGaussianFunction()	Constructs an instance.

Method Summary

Modifier and Type	Method	Description
double[]	gradient(double x, double[] parameters)	Computes the gradient vector for a four variable version of the function where the parameters, a, b, c, and d, are considered the variables, not x.
double	value(double x, double[] parameters)	Computes value of function f(x) for the specified x and parameters a, b, c, and d.

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

ParametricGaussianFunction

public ParametricGaussianFunction()

Constructs an instance.

Method Detail

value

public double value(double x,
                    double[] parameters)
             throws ZeroException

Computes value of function f(x) for the specified x and parameters a, b, c, and d.

Specified by:

value in interface ParametricRealFunction

Parameters:

x - x value

parameters - values of a, b, c, and d

Returns:

value of f(x) evaluated at x with the specified parameters

Throws:

IllegalArgumentException - if parameters is invalid as determined by validateParameters(double[])

ZeroException - if parameters values are invalid as determined by validateParameters(double[])

gradient

public double[] gradient(double x,
                         double[] parameters)
                  throws ZeroException

Computes the gradient vector for a four variable version of the function where the parameters, a, b, c, and d, are considered the variables, not x. That is, instead of computing the gradient vector for the function f(x) (which would just be the derivative of f(x) with respect to x since it's a one-dimensional function), computes the gradient vector for the function f(a, b, c, d) = a + b*exp(-((x - c)^2 / (2*d^2))) treating the specified x as a constant.

The components of the computed gradient vector are the partial derivatives of f(a, b, c, d) with respect to each variable. That is, the partial derivative of f(a, b, c, d) with respect to a, the partial derivative of f(a, b, c, d) with respect to b, the partial derivative of f(a, b, c, d) with respect to c, and the partial derivative of f(a, b, c, d) with respect to d.

Specified by:

gradient in interface ParametricRealFunction

Parameters:

x - x value to be used as constant in f(a, b, c, d)

parameters - values of a, b, c, and d for computation of gradient vector of f(a, b, c, d)

Returns:

gradient vector of f(a, b, c, d)

Throws:

IllegalArgumentException - if parameters is invalid as determined by validateParameters(double[])

ZeroException - if parameters values are invalid as determined by validateParameters(double[])